How to find ACF, PACF, Sample Variance-Covariance Matrix of Random-Effects?

Can you give an example please?

   The covariance matrix is typically (for nlme and other packages that 
follow the same conventions) extracted with VarCorr().  As described in 
my other e-mail to the list, this is not *quite* the same as the full 
covariance matrix of the random-effects vector, but rather the 
covariance matrix for a single grouping variable/block.  VarCorr() 
returns a list.  So e.g. if

library(lme4)
fm1 <- lmer(Reaction ~ Days + (Days|Subject), sleepstudy)


VarCorr(fm1)$Subject gives a 2x2 covariance matrix

cov2cor() will convert this to a correlation matrix.

Or, for lmer fits at least, the correlation is already present as an 
attribute:

attr(VarCorr(fm1)$Subject, "correlation")

Dear All,

I am writing to ask how to compute the (partial) autocorrelation of random-effects versus lag, and sample-variance covariance matrix of the random-effects given some data without specification of some model or structure on the random-effects covariance matrix.

Best regards,
John

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Dr. Benjamin Bolker
Professor, Mathematics & Statistics and Biology, McMaster University
Director, School of Computational Science and Engineering
(Acting) Graduate chair, Mathematics & Statistics
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